Time-interleaving of two, or more, analog-to-digital converters (ADCs) is a common way to overcome the limits of hardware technology that affect the maximum sampling frequency fS for a single ADC. Time-interleaved analog-to-digital converters (TI-ADCs) offer a significant increase in the available sample rate of ADCs. In other words, for example, by using two TI-ADCs operating in parallel with a Ts time offset of their 2Ts time interval sampling clocks (i.e. a 180-degree phase shift in the sampling clocks), the overall sampling frequency of the system is doubled. In an ideal two-channel TI-ADC, aliasing terms formed by the individual ADCs, operating at half rate, are cancelled by the interleaving process. This canceling occurs because the aliased spectral component of the time offset ADC has the opposing phase of the same spectral component of the non-time offset ADC. In the absence of time offset and gain mismatch the sum of their spectra would cancel their alias components.
The performance of TI-ADCs is degraded by timing and gain mismatches. Most of the prior art on mismatch estimation and correction in TI-ADCs is concentrated on low-pass converting base-band signals. Modern system designs lean towards having the TI-ADC interface with intermediate frequency (IF) centered signals in the analog section of a digital receiver rather than the DC (base-band) centered, analog down converted, in-phase and quadrature pair. In many cases the IF is located above the fS/2 and the sampling process directly down-converts the band-pass input signal to the frequency range from 0 to fS/2. This process is called sub-sampling or band-pass sampling.
The sample instants of the individual time-interleaved ADCs are affected by an unknown and possibly slowly varying with environment time delay, Δtm, which results in an undesired frequency dependent phase offset of their aliased spectra that prevents their perfect cancellation at the output of a time multiplexer. Mismatches in path gains, gm, of the TI-ADC, due to the tolerance spread of analog components, are always present in the ADC's hardware. The gain mismatch contributes a non frequency dependent imperfect cancellation of the spectral components at the output of the TI-ADC system.
In order to correct the artifacts caused by the time and gain offsets, the artifacts must first be estimated. Estimation methods can be divided in two categories:                Foreground techniques, also known as non-blind techniques, that inject a known test or probe signal to estimate the mismatches by measuring the TI-ADC output responses to the probe; and        Background techniques, also known as blind techniques, for which no information is required about the input signal (except perhaps for some knowledge about the presence or absence of signal activity in certain frequency bands) in order to estimate the mismatches.The first approach has the disadvantage that normal TI-ADC operations are suspended during the probe while in the second approach the calibration process does not interrupt normal operation.        
In other words, a common problem is the removal of undesired signal artifacts related to timing and gain imbalances between interleaved analog-to-digital converters. This problem is addressed by a number of algorithmic approaches. These include direct and indirect approaches. In the direct approach, spectral artifacts related to timing imbalance are detected and the timing clocks are adjusted in the direction that reduces the size of the spectral artifacts. In the indirect approach, spectral artifacts related to timing imbalance are detected and the converter's digital samples are altered in adaptive filters to reduce the size of the spectral artifacts. Similarly, spectral artifacts related to gain imbalances are detected and the gains of the analog paths are altered to reduce the error size in the analog domain (direct approach) or the converted samples are gain corrected in the sampled data domain to reduce the error size related to gain imbalance.
The existing timing skew correction structures for time-interleaved ADCs work only for analog input signals that are located in the first Nyquist zone (i.e. between 0 and fs/2). Such solutions can be based on digital filters with fractional sample delay or use a canceling structure based on a derivative filter.
A prior art detection and correction structure 100 for a two channel TI-ADC is shown in FIG. 1. The basic idea in this case is generally based on the recognition that when the analog signal is sampled, the timing skew causes an error that is approximately proportional to the signal derivative multiplied by the timing skew. This approximation holds well when the skew is small compared to the inverse of the signal frequency, which is generally true. The correction structure creates an estimate of the error signal 101 and subtracts it from the TI-ADC output signal 102. The error signal estimate 101 is generated by taking a derivative (at 103) of the digital TI-ADC output signal 102 and using an LMS (least mean square) algorithm (at 104) to find an estimate for the timing skew.
In the sampled domain signals only up to fS/2 can be uniquely represented. For instance, two signals at different frequencies f and fS+f in the continuous time domain (TI-ADC input) both appear at the same frequency f in the sampled domain. This is illustrated in FIGS. 2-4, which show the spectrum of the TI-ADC input signal (analog domain) and the spectrum of the corresponding TI-ADC output signal (sampled domain). One can see that input signal in the range from 0 to fS/2 (FIG. 2) results in an output signal that is identical to one produced by an input signal in the range from fS to 3fS/2 (FIG. 4). An input signal in the range from fS/2 to fS (FIG. 3) undergoes the same down conversion process, but with additional spectral inversion.
For the reason described above the output of the derivative filter 103 (FIG. 1) operating on the sampled data used in the prior art correction method can reasonably match the derivative of the analog signal only when its highest frequency component is less than fS/2.